Brush him frequently. Theoretically, that will cut down on the fur everywhere, and cut down on the hairballs / puking. Unfortunately for me, mine hates being brushed (any attempt ends up with a bloody hand). I have had limited success with one of these, but as soon as he realizes there is brushing involved, he starts attacking it.
I have that problem too. The best thing I've tried is the True Touch Deshedding Glove:
https://www.amazon.com/True-Deshedding-Gentle-Efficient-Grooming/dp/B01D1ZULK4
I have another similar glove that does almost nothing... This one is actually pretty good compared to that and other things I've tried like combs and a few different kinds of pet brushes.
My bunnies seem to really like how this glove feels too. ��